Video: Comparing Fractions and Percentages in a Real-World Context

William has been offered a discount at the local diner since he always has his breakfast there on work days. He can either have 1/5 or 30% off his next meal. Which offer should William take?

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Video Transcript

William has been offered a discount at the local diner since he always has his breakfast there on workdays. He can either have one-fifth or 30 percent off his next meal. Which offer should William take?

Since these are discounts, this will be money that should be subtracted from the price. So William is essentially saving money. So which discount will help him save the most money, one-fifth off the price or 30 percent off the price?

So essentially, we are comparing one-fifth, a fraction, to 30 percent, a percentage. Let’s go ahead and make the fraction and the percentage both be a decimal so we can compare them.

In order to write one-fifth, the fraction, as a decimal, we need to take the numerator, which is the number on top, and divide by the denominator, the number on the bottom. So in our calculators, we should type one divided by five equals. And we get 0.2.

So now let’s convert the 30 percent to a decimal. So the first thing that we need to do is to get rid of the percentage sign. So we just have 30. We can go ahead and write in our decimal point because we’re going to have to move it two places to the left, one two, so .30.

Now when there’s nothing to the left of the decimal point, it’s a good idea to place a zero to the left of that decimal point so that with a decimal point is seen better. So we have 0.30. So we’re comparing 0.2 and 0.30. So the two doesn’t have a zero after it. However, it would be one hundred percent okay to add a zero to the end. It doesn’t change the value.

So which discount would be larger, 0.20 or 0.30? It would be the 0.30. Therefore, William should take the 30 percent discount. It’s a larger discount. So he will be saving more money.

Now as we have looked at 0.20 compared to 0.30, it would have been okay to take away the zero on the end because it doesn’t change the value. So we could’ve compared 0.2 and 0.3. Again, our answer would still be the 0.3 is larger. So once again, William should take the 30 percent off discount.

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